Please, if you know, why the latest supported FPGA firmware by YateBTS for bladeRF x40 is 0.1.2? I don't think it is good to use so old version. But when I try to use the newer firmware, I instantly get radio tune error and yate don't start.

The Yate project implemented their own driver to directly control the bladeRF's hardware, bypassing our C library entirely. Since it's built to control a specific version of the FPGA, it will not work with newer FPGA versions (which use a different control interface) without significant overhaul.

That said, it is okay to use an older FPGA version (even a much older version) for a specific application. You can still auto-load a newer FPGA for libbladeRF-based applications.